Supercurrent structures utilizing mobil flux vortices

ABSTRACT

A supercurrent logic structure of extended dimensions is capable of sustaining a plurality of trapped magnetic field vortices each of which supports one flux quantum. Such a vortex prefers to position itself in a region such that a local minimum of the sum of the magnetic energy plus the Josephson coupling energy is established. A variety of ways to create such preferred regions are disclosed. A vortex is moved from one such region to another in shift register fashion by applying a force thereto as, for example, by applying a local current or magnetic field near to the vortex.

United States Patent Anderson et al.

[151 3,676,718 51 July 11,1972

[54] SUPERCURRENT STRUCTURES UTILIZING MOBIL VORTICES [72] Inventors: Philip Warren Andels on, New Vernon; Robert Carr Dynes; Theodore Alan Fulton,

both of Berkeley Heights, all of NJ.

[73] Assignee: Bell Telephone Laboratories, Incorporated,

Murray Hill, NJ.

[22] Filed: March 26, 1971 21 App1.No.: 128,445

[52] U.S. Cl ..307/306, 307/221, 307/277, 317/234 T [51] Int. Cl ..I-l03k 3/38, G1 1c 19/00 [58] Field of Search ..307/212, 221, 277, 306; 317/234 T [56] References Cited UNITED STATES PATENTS 3,238,514 3/1966 Marchand ..307/306 X 3,458,735 7/1969 Fiske ..307/2 1 2 X 3,478,230 ll/l969 Otter, Jr. et al.. ....307/306 X 3,522,492 8/1970 Pierce ....307/306 X 3,588,577 6/1971 Schroen ..307/306 X Primary Examiner--John Zazworsky Attorney-R. J. Guenther and Arthur J. Torsiglieri ABSTRACT A supercurrent logic structure of extended dimensions is capable of sustaining a plurality of trapped magnetic field vor-, tices each of which supports one flux quantum. Such a vortex prefers to position itself in a region such that a local minimum of the sum of the magnetic energy plus the Josephson coupling energy is established. A variety of ways to create such 1 preferred regions are disclosed. A vortex is moved from one such region to another in shift register fashion by applying a force thereto as, for example, by applying a local current or magnetic field near to the vortex.

41 Claims, 16 Drawing Figures SUPERCURRENT STRUCTURES UTILIZING MOBIL FLUX VORTICES BACKGROUND OF THE INVENTION This invention relates to weak-link supercurrent structures and, more particularly, to such structures capable of sustaining trapped magnetic field vortices.

In the early stages of the superconductive art the basic switching device was the classical cryotron a current controlled device capable of being switched between a superconducting state and a normal conducting state. As the art progressed, more sophisticated switches such as the Josephson junction were developed. The Josephson junction, as well as the now well known SNS, point contact and bridge configurations, are characterized by the ability to sustain a supercurrent at zero voltage up to a certain maximum critical current J,., and by a normal" superconducting state at a finite voltage. Such devices are now described as weak-link devices. Switching between these states is typically efiected by varying an applied current above and below J, or by fixing the applied current and varying a magnetic field which in turn changes J The basic Josephson junction and its aforementioned properties are described in U.S. Pat. No. 3,281,609 issued to J. M. Rowell on Oct. 25, 1966 and assigned to the assignee hereof. Improved'forms of weak-link devices are disclosed in U.S. Pat. No. 3,564,351 issued to D. E. McCumber on Feb. 16, 1971, also assigned to the assignee hereof. In addition, the superconductive totalizer or analog-to-digital converter disclosed in U.S. Pat. No. 3,450,735 issued on July 29, 1969 to M. D. Fiske is exemplary of the prior supercurrent art in which binary information is represented by a Josephson junction being in either its supercurrent-zero voltage state or its normal superconducting-finite voltage state.

It is an object of our invention, however, to represent logic information in a plurality of coupled weak-link devices, or in a plurality of coupled weak-link regions of an extended single junction device, which during operation remain in a supercurrent state.

It is another object of our invention to represent such information by a plurality of trapped magnetic vortices capable of being controllably created or annihilated at preferred locations in a logic device.

It is another object of our invention to controllably move such vortices in shift register fashion from one such preferred location to another.

SUMMARY OF THE INVENTION These and other objects are accomplished in an illustrative embodiment of our invention, a weak-link supercurrent logic structure which is able to sustain one or more trapped magnetic field vortices. In an extended Josephson junction device which is large compared to the Josephson penetration depth M), such a vortex is induced by a spatial variation of the supercurrent J(x) in which a positive supercurrent flows through the oxide layer and into the contiguous superconductor to a depth M, the London penetration depth, then along the superconductor a distance of about 2%,, thence through the oxide again as a negative supercurrent into the opposite superconductor to a depth A and finally back to the point of beginning. Such a vortex supports a net magnetic flux of precisely I 2.07 X Wk, the well-known flux quantum. Hereinafter, the term "vortex" shall define an entity which includes both the circulating supercurrent J(x) and the flux quantum D, induced thereby.

Once a vortex is created it prefers to position and distribute itself in a region so that a local minimum of the sum of the magnetic energy plus the Josephson coupling energy is established. Where a plurality of such preferred locations are present in a single weak-link structure, it is possible to move the vortex from one such location to another by applying a force thereto as, for example, by applying a local current or magnetic field to a region near to the vortex.

A number of ways are hereinafter described to create such preferred locations including, for example: (1) creating regions in the structure at which J (x) 0, e.g., by intentionally fabricating the oxide with gaps in it, thereby forming a structure having periodic oxide regions; a similar structure may also be fabricated utilizing discrete isolated junctions connected in parallel; (2) fabricating the oxide of a variable thickness to create regions of variable J (x) in a fashion similar to (1) above; (3) applying a local point source of magnetic field at periodic locations along the oxide layer; (4) applying a local current at periodic locations along the oxide layer to create a local magnetic field analogous to (3) above; and (S) fabricating the structure such that it has a variable self-inductance per unit length, e.g., in top view the width of the device undulates in a prescribed manner such that a vortex prefers to position itself about a region of minimum width.

In a similar fashion vortices and preferred locations can be created in other types of weak-link structures. As used herein, the term weak-link structure includes, but is not limited to, not only a structure having a single uniform weak-link region (e.g., structures (3), (4) and (5) supra) but also a structure having a plurality of smaller separated weak-link regions connected in parallel e.g., structures I) and (2) supra).

BRIEF DESCRIPTION OF THE DRAWING These and other objects of the invention, together with its various features and advantages, can be more easily understood from the following more detailed description taken in conjunction with the accompanying drawing, in which:

FIG. 1 is an end view of a typical Josephson junction;

FIG. 2, Parts A E, indicate the gradual change in supercurrent spatial distribution as applied current is increased;

FIG. 3A shows schematically a trapped vortex having a supercurrent J(x) and a magnetic field B;

FIGS. 38 and 3C are graphs of the approximate distribution of vortex magnetic field in the junction of the devices of FIG. 3A;

FIGS. 4A-4C are end views of a Josephson junction structure in accordance with an illustrative embodiment of our invention in which a hole in the oxide creates a region where J,

FIG. 5 is an isometric view of a second embodiment of our invention utilizing discrete Josephson junctions;

FIG. 6 is an end view of a third embodiment of our invention in which the oxide layer is of variable thickness;

FIG. 7A is an end view of a fourth embodiment of our in- .vention utilizing point sources of magnetic field to create preferred vortex locations;

FIG. 7B is an en view of a fifth embodiment of our invention in which preferred locations are made to propagate;

FIG. 8 is an end view of a sixth embodiment of our invention utilizing current sources to create preferred vortex locations;

FIG. 9 is an isometric view of a seventh embodiment of our invention utilizing variable self-inductance to create preferred vortex locations;

FIG. 10A is a top view of a working example of our invention utilizing a pair of the devices of FIG. 5 connected in parallel; and

FIG. 10B is a schematic of FIG. 10A.

DETAILED DESCRIPTION Before discussing in detail the various embodiments of our invention, it will be helpful to consider the spatial buildup of supercurrent in an SIS Josephson junction and the subsequent creation of a trapped magnetic field vortex. An SIS Josephson junction is depicted for the purposes of illustration only, it being understood that the following comments apply equally as well to other types of weak-link structures.

Turning then to fig. I, there is shown an end view of an elongated Josephson junction structure 10 of length I the Josephson penetration depth. The structure 10 is multilayered including an oxide layer 12 (e.g., PbO) formed between a pair of superconductive layers 14 and 16 (e.g., Pb). A current source 18 is connected across the superconductors at he lefthand edge 19.

As the current from source 18 is increased, the supercurrent J(x) penetrates farther and farther into the device from left to right until at some current I 1,, as shown in FIG. 2, Part A, the maximum supercurrent is at the left-hand edge (x O) and the distribution J,(x) gradually decreases to zero at a distance A, from the left-hand edge. Note that in FIG. 1, as well as in embodiments to be subsequently described, the supercurrent is shown on the end face for the purpose of clarity only. In practice, the supercurrent would be interior to the device and generally located opposite the contacts of source 18. -As the current is increased further, the point of maximum J(x) moves away from the left-hand edge and to the right, as shown in FIG. 2, Parts B and C. In fact, at I 1 the supercurrent flows across the junction in both directions as represented by the positive and negative values of J (x) in FIG. 2, Part D.

At this point it should be noted that the spatial supercurrent distributions J,(x) to J,(x) are fixed in space. At a current I 1 1,, (FIG. 2, Part E), however, a limit is reached where the supercurrent distribution cannot adjust itself to carry additional current. Consequently, an incipient vortex is formed which propagates to the right at a velocity, and to a distance, determined by damping processes (e.g., single particle tunneling). Simultaneously, another vortex begins to form at the lefthand edge as described with reference to FIG. 2, PartsA The process is repeated until other factors intervene, e.g the applied current is reduced or a propagating vortex stops ata preferred location somewhere between the left and right-hand edges. Techniques for creating such preferred locations will be discussed hereinafter.

A schematic of an isolated vortex is shown in FIG. 3A, where it has been assumed that the vortex is stationary at some arbitrary preferred location designated 20. From point 20 where J(.r) 0 the supercurrent increases (positively and negatively) on either side thereof to a distance A, (typically about 100 p in SIS devices, but typically considerably shorter in SNS and other weak-link devices) so that the total length of the spatial distribution of J(x) extends over a length of about 2%,. This current tunnels from one superconductor to the other through the oxide layer penetrating to a depth A the London penetration depth (typically about 0.l p. is SIS devices). As shown, the lateral skin current flows in each superconductor parallel to the oxide layer 12 but in opposite directions thus forming a closed supercurrent loop centered at point 20. This current supports precisely one magnetic flux quantum 1 2.07 X Wb which extends through'the oxide layer from one end face 19 to the other (not shown) closing upon itself through space. The magnetic field 8,. associated with the vortex is related to 1 by the well-known relation that where A is the area bounded by J(x). For simplicity only, 8,. is shown in FIG. 3A as consisting of a single closed flux line. In actuality, in the x-direction along the junction, B,.(x) is approximately Gaussian in shape as shown in FIG. 33, whereas in the z-direction across the junction, B -(z) is uniform in the oxide and decays exponentially to a distance of about A as shown in FIG. 3C.

A vortex once created as previously described will prefer to position and distribute itself in a region such that a local minimum (not necessarily an absolute minimum) of the sum E of the magnetic energy E,,, plus the Josephson coupling energy E, is created, i.e., a minimum ofE= E,, E, given by all ace 211' lane of junction The first term on the right-hand side of Equation l is E,,. and the second is E where u, is the permeability of free space, E is the total magnetic field equal to B B,., where B is the magnetic field other than that of the vortex and 8,. is the magnetic field associated with the vortex; V is volume, 1 is the flux quantum; J (x,y) is the critical supercurrent density in the junction (x,y) plane; and (x,y) is the spatially dependent phase difference between the wave-functions in the superconductors on either side of the junction.

In effect, a vortex seeks out" regions in which this minimization can be accomplished. Once located in such region, a vortex will remain there until a force is applied to the vortex as described hereinafter.

Consequently, it is desirable to construct a device so that vortices can distribute themselves to minimize E, and/or to maximize E, (since its contribution to E is negative). Of course, trade-offs may be required since in a particular structure the position of a vortex in a particular region may, for example, both decrease E,, and decrease E or conversely may both increase E, and increase E,,,. In the latter cases, therefore, the relative magnitude of changes should be considered. Utilizing the above criteria, we have determined that preferred vortex locations may be created in a number of illustrative ways, to wit:

A. by fabricating a weak-link structure with one or more regions where J 0, as by the use of discrete Josephson junctions;

B. by fabricating an oxide layer of a Josephson junction, for

example, to have a thickness which varies in the z-dimension along the layer;

C. by utilizing a uniform junction and point sources of mag-- netic field placed at periodic points along the junction to establish a field in opposition to B,.; D. by utilizing locally applied currents to establish the field of (C) above; E. by fabricating the weak-link structure to have a variable self-inductance per unit length. Before describing each of the foregoing illustrative embodiments, however, the determination of the separation between preferred locations will be discussed.

PREFERRED LOCATION SPACING In a uniform extended junction (e.g., FIGS. 3A,-7A, 8) in order to support flux vortices the appropriate separation of adjacent preferred locations is about 2A,. On the other hand, in a nonuniform junction (e.g., FIGS. 4C, 5, 6) the appropriate separation S is determined as follows: given an extended structure having arbitrary spacing S between tentatively selected preferred locations, but otherwise having a fixed geometry, one can readily calculate numerically in a wellknown fashion the extent and precise form of a supercurrent distribution J(x,y) which will support a single quantum of flux b i.e., the formof a vortex in such a structure can be determined. This calculation is performed by utilizing Josephsons equations (see, for example, Physical Review, 41, 2,047 (1970) by C. S. Owen and D. J. Scalapino), as they relate the spatial variation of (x,y) to magnetic fields, in conjunction with Maxwells equations relating the supercurrent flow to the magnetic field distribution.

Having thus chosen an arbitrary S and calculated the vortex shape, one compares the two. If the vortex dimension in the xdirection is substantially larger than the spacing S, the calculation is iterated for a smaller S until a value of S is determined which is substantially equal to the vortex dimension in the xdirection. Conversely, if a value S were initially chosen to be too large, it is possible that more than one vortex could exist within a region of length S, a possibility which can readily be checked by numerical calculation. If so, a smaller S should be chosen until, again, it matches the vortex dimension in the xdirection. Precise equality is not, however, required as long as S is chosen to confine a single vortex.

To a first approximation, the preceding criterion is equivalent to satisfying the relationship L c=o (2) where L is the self-inductance of a typical supercurrent loop which supports a single flux quantum 1 and I is the net critical current of a region of the device of length S.

EMBODIMENT A: REGIONS WHERE J,.=

One way to create a region where J, 0 is to form the oxide layer 12, as shown in FIG. 4A, with a hole 22 therein extending between the superconductors. Accordingly, the supercurrent J(x) centers itself on the hole with current flowing in opposite directions on either side thereof. The flux I (not shown) is directed into the page and is substantially confined in the hole 22.

To appreciate qualitatively the reason that the vortex prefers to sit on the hole it must be recognized that the right hand term (E of Equation (1) would be a maximum if cos d: equaled unity (d) 0, 211) everywhere in the junction. However, the presence of a magnetic field B( y) in the y-direction, for example, either from an external source or the vortex itself, causes (I) to vary spatially in the x-direction because the derivative dldx is proportional to B(y). Consequently, the presence of a vortex alone dictates that 4) cannot be zero everywhere in the x-dimension. In fact, with reference again to FIG. 3A, cos 4) l at points 21 and 23, the extreme edges of J(x) and cos d: l at the center 20. At intermediate points cos 11) takes on values between +1 and -I. Since (1) varies with x, it follows that cos (1) does also. To increase E I it would be desirable to reduce the contribution of the regions corresponding to values of cos 4: l (e.g., negative contributions of regions where cos (b 0). One way of effecting this result is to locate the center of the vortex at a point where J, 0 since E, involves the product of J,(.\',y)cos (x,y). Consequently, the negative contributions to E, are eliminated, E, is increased and, as desired, E is decreased.

Consider now that the hole is made wider as shown at 24in FIG. 48. Since no supercurrent can flow in the hole, the distribution J(x) accommodates the hole by increasing its density in the extreme regions at 26 and 28. Note that the device of FIG. 4B is beginning to resemble two discrete junctions, one on either side the hole 24. Ultimately, as shown in FIG. 4C, a structure having a plurality of such holes 24 between discrete oxide regions 30 will support a plurality of vortices, one centered on each hole. As discussed previously, the oxide regions are separated by a distance S calculated to satisfy equation (2). Therefore, a single flux quantum is induced by each supercurrent loop 32 flowing between adjacent oxide regions 30. Note also that supercurrent from adjacent vortices may flow through a common junction in opposite directions, thereby producing substantially total cancellation of the supercurrent therein. Thus, adjacent loops 32.1 and 32.2 flow through common junction 30.2 producing substantially total cancellation. The loop, therefore, in effect extends between junctions 30.1 and 30.3 and supports two vortices, one centered at point 24.1 and one at point 24.2.

Instead of utilizing holes in an otherwise uniform junction structure to create preferred vortex locations, it is possible as shown in FIG. to utilize a discrete junction configuration which satisfies Equation (2). In this case the hole is created by fabricating a U-shaped superconductor 40 on the end portions of which are formed discrete oxide layers 42 and 44. Subsequently superconductor 46 is deposited to join the oxide layers, thereby forming a pair of Josephson SIS junctions electrically connected in parallel. Current source 48 causes a supercurrent J(x) to flow in path shown by the dashed line. This supercurrent supports a magnetic field 8,. which threads the hole 50 formed by U-shaped superconductor 40 and superconductor 46. The use of this type of device in a shift register will be described hereinafter with reference to FIGS. A and 10B.

EMBODIMENT B: VARIABLE INSULATOR THICKNESS Recognizing that thick insulator regions (e.g., about A. thick) also produce regions where J 0 (since electron pair tunneling is effectively prevented), it follows that a structure such as shown in FIG. 6 will support a plurality of trapped vortices. More specifically, an insulator, such as oxide layer 12, is fabricated with a plurality of thin oxide regions 62, each capable of carrying a supercurrent, separated from one another by thick oxide regions 60 in each of which J 0. As before the thin oxide regions 62 are spaced from one another by a distance S calculated to satisfy Equation (2). Accordingly, a single vortex prefers to center itself on a thick oxide region 60 with the supercurrent J(x) flowing through adjacent thin oxide regions (i.e., the operative junctions).

EMBODIMENT C: POINT SOURCES OF MAGNETIC FIELD In FIG. 7A there is shown a cross-sectional view of a twostage Josephson shift register in accordance with an illustrative embodiment of our invention in which a substantially uniform oxide layer 59 is sandwiched between a pair of elongated superconductive layers 63 and 64. Vortices are created by means of current source 61 connected across the superconductors 62 and 64 at the left-hand edge 57. Illustratively, a pair of preferred vortex locations 66 and.68 are established by directing at each of these locations an external magnetic field B generated by point sources 70 and 72. The magnetic sense of B is made to be opposite of that of 8,. thereby reducing the total field B B B,.. Since E is thereby reduced, vortices distribute themselves around points 66 and 68 so that local minima of Equation (1) are created. Since FIG. 7A depicts a uniform junction, joints 66 and 68 are separated by about 2X, to satisfy Equation (2).

In order to cause the vortices to propagate to the right, a current source 74 is selectively connectable by means 52, switches 75 and 77 to points 52 and 54 intermediate each vortex location. With switch 77 closed a current 1 flows across the junction in a region adjacent to the right-hand side of supercurrent loop J (x). The current 1 flows in the same direction as J (x) does in region 69. As a result, J (x) will shift to the right (toward 1 At the extreme right-hand end the vortex is detected by utilization device 76, typically a weaklink double junction magnetometer, (or alternatively a voltmeter) connected across the right-hand end of superconductors 63 and 64. Note that both vortices may be moved together by closing switches 75 and 77 simultaneously. In addition, adjacent vortices can be moved simultaneously if I, is sufiiciently large (thus J pushes J to the right). Care should be exercised, however, since too much control current I may drive the junctions into a finite-voltage state. Moreover, whereas control current flows between preferred vortex locations, as at point it should be made to flow much nearer to the preferred vortex location it is designated to control than to the adjacent vortex location, e.g., since I is designated to control J point 52 should be closer to vortex location 66 than location 68.

A similar embodiment is shown in FIG. 7B. The sequential application of point sources of magnetic field generated by control sources Ml-M3, MlM3' and Ml"-M3", causes the preferred vortex locations, and thus the vortices themselves to propagate. For example, with only Ml-M3 ON, the preferred locations are designated by an x at locations Pl-P3, respectively. If now Ml'-M3' are also turned ON (and then Ml-M3 turned OFF), the preferred location moves to the right to intermediate positions Pl'-P3'. Consequently, vortices originally centered at P1-P3 move to P1'-P3', respectively. Similarly, activation of M1-M3" causes vortices to move to the left to Pl-P3", respectively. This form of control can be applied equally as well to the other embodiments of our invention.

EMBODIMENT D: CURRENT SOURCES TO GENERATE ea-l As discussed above with reference to Embodiment C, FIG. 7A, point sources of magnetic field B applied at periodic locations along the oxide layer define preferred vortex locations provided the sense of B is opposite to that of 8,. in the oxide. In FIG. 8, the point sources 70 and 72 of FIG. 7A have been replaced by local current sources 80 and 82, respectively. The resultant current flow in oxide layer 59 from sources 80 and 82 generates at each preferred location a local magnetic field 8 Tee operation and structure of this embodiment are otherwise identical to that of FIG. 7A. In addition, however, an alternate form of vortex source means is shown. Current source 61, instead of being connected across superconductors 63 and 64, is connected across an inductor 65 which is positioned to produce a magnetic field at point 66 near to the lefthand end and in the plane of the junction. This field in turn induces a circulating supercurrent J(x). Either of these source means may be used interchangeably with each of the embodiments of our invention.

EMBODIMENT E: VARIABLE SELF-INDUCTANCE In FIG. 9 there is shown an illustrative embodiment of our invention comprising a first portion 84, where J (x,y) is uniform and nonzero, and asecond laterally contiguous portion 86 where J (x,y) and the self-inductance per unit length is variable. The self-inductance per unit length L(x) of the combined portions is therefore also variable.

More specifically, portion 84 illustratively comprises a uniform Josephson junction having an oxide layer 91.1 of uniform thickness sandwiched between superconductive layers 93.1 and 95.1. Portion 86 is similarly constructed except that oxide layer 91.2 is thicker in order that I, be made zero therein.'ln addition, the width of portion 86 is made variable as measured in a direction (y-axis) normal to the direction of vortex propagation (x-axis). To produce a variable L(x) at least one edge 90 parallel to the direction of propagation -is made to have an undulating, preferably periodic, shape. As shown in FIG. 9, edge 90 illustratively has a square wave shape. A current source 92 connected across superconductors 93.1 and 95.1 creates a supercurrent flow across the junction and generates trapped vortices as previously described. These vortices prefer to position themselves at points 96 of minimum width (i.e., in the notches). As before, current from control source 94 is applied to regions 89 intermediate preferred vortex locations 96 to shift the vortices to the right, selectively or simultaneously, depending on the manner in which switches 87 are closed. Of course, the device of FIG. 9 may also be symmetrical by fabricating on one end face 88, a structure which is a substantial mirror image of portion 86.

In order for this embodiment to operate effectively in trapping vortices in the notches 90.2, it is important that the notch separation s be properly chosen. In devices in which the undulations take on complicated shapes, a proper s would be calculated by numerical analysis to satisfy Equation (2). However, the embodiment of FIG. 9 utilizes a simplified undulating shape, a square wave, in which the maximum width (y-dimension) is 2w, the minimum width (in a notch 90.2) is w, the width of a notch is s and the notches are separated from one another by a distance .r. In this structure the self-inductance per unit length L in the notches 90.2 is given by .+d /w (3) where n is the permeability of free space, A, is the London penetration depth and d is the oxide thickness in portion 86. In the wide sections 90.1 the inductance per unit length is onehalf Equation (3).

When sis properly chosen, a vortex will position itself in the center of a notch 90.2 and extend on either side thereof. The supercurrent flow I of the vortex is, with a factor of about 2, equal to J (the approximation arises because (x,y) depends on position in the notch so that sin 4) 7 l in the entire notch).

Moreover, the supercurrents on the average will circulate around a loop of approximately length s centered in a notch so that the loop inductance is approximately 11,0) d)s/w.

Since Equation (2) dictates that LI= b s to a first approximation is given by That the vortices prefer to sit in the notches, which are points of high self-inductance per unit length, can be understood by reference to the E term of Equation (1). More specifically, the magnetic field of the vortex, which is mainly concentrated in a notch, has a value 8,. [L l/W, where is the permeability of free space, I is the supercurrent associated with the vortex and w is the width of thestructure in a notch. Since w is smaller in a notch, 8,. is larger thereby disadvantageously increasing the value of B in the 15,, term. However, the spatial extent of the vortex in the x-direction is smaller in a notch which more than compensates for the larger B contribution. Another way of viewing this principle is to recognize that the magnetic energy E is approximately equal to d ,,-l. In the notches a higher self-inductance prevails so that the current I required to support 1 is smaller.

EXAMPLE A two-loop, three-junction shift register as shown in FIG. 10A has been successfully constructed and operated as follows.

On a rectangular glass substrate 102 there was evaporated a rectangular Sn film 104 filling the central portion of the substrate to serve as a superconducting ground plane. Both the Sn and glass were then covered with an evaporated germanium film (not shown) to electrically insulate the ground plane. The region of the ground plane forms the surface on which were evaporated the thin films which form the actual shift register.

On the ground plane 104 there was next deposited an evaporated Sn film 106 having an elongated central member 106a, three equally spaced (by a distance of about 3 mm) appendages 106 (b-a') on one side thereof, and five appendages 106 (e-i) on the other side thereof. Thereafter the surface of the Sn film 106 was oxidized in a glow discharge of oxygen. Subsequently, evaporated Sn strips 107, 108 and 109 were deposited so that strip 108 coupled members 106:: and l06f, strip 109 coupled members 106k and 106i and strip 107 coupled members 106b, 1060 and 106d. Josephson junctions were thus formed at the regions of overlap between film 106 and strips 107, 108 and 109. The configuration of the junctions and the loops 113 and 114 were adapted to satisfy Equation (2). In a final evaporation, silver shunts 110, 111 and 112 were deposited in parallel with each of the junctions.

In FIG. 10B the pattern of the films 106 to 109 of FIG. 10A is shown schematically. The circles E, F and G designate the three junctions which, together with the two large right-hand loops 113 and 114 comprise a two-stage shift register (using structures of the type shown in FIG. 5). The other junctions, designated A, D, K and L comprise two separate double-junction interferometers (magnetometers) which were used to monitor the magnetic flux contained in the loops 113 and 114 of the shift register. More specifically, the junction pair A-D comprises a magnetometer to monitor loop 113 and junction pair K-L comprises a magnetometer to monitor loop 114. The two magnetometer loops are designated 115 and l 16. Current leads were attached at the various numbered points number 1 to 10.

In our structure the Sn films were of the order of 1,000 A.

thick and the Ge film wasabout 10,000 A. thick. The ground plane was about 1 cm by cm and the upper films 106-109 were about 0.2 mm wide and a few mm long. The dimensions of the various loops were about l3 mm by l-3 mm.

The entire structure was cooled in liquid l-Ie below the superconducting transition of Sn, and was shielded from the earth's magnetic field by well-known mu-metal. Sn was chosen because oxidation thereof is relatively easy. In practice Pb, Nb or Ta which are superconducting at 4.2 K. may also be used.

The l-V curves of the two magnetometers were displayed on an oscilloscope by applying current and measuring voltage between leads 7 and 8 and between leads 9 and 10 for the magnetometers A-D and K-L, respectively. The critical supercurrents of these magnetometers depend upon the magnetic field linking the loops 115 and 116. Since any flux supported in, say, the register loop 113 requires a current flowing around that loop, and in particular through the portion BC, some fiux from that loop will also link the A-D magnetometer loop 115. Thus, the critical supercurrent of magnetometer A-D is affected by any flux present in the register loop 113, and one may observe changes in this flux as changes in the critical supercurrent of the magnetometer.

In the structure built the self-inductance of each register loop 113 and 114 was about 2Xl0' l-l, and of each magnetometer loop 115 and 116 about 4 l0'"H. The critical supercurrents of the magnetometers were about 50 4A, depending on temperature and other factors. The coupling between the magnetometer loops and the register loops was about 0.2, i.e., one-fifth of the flux trapped in a register loop linked a magnetometer loop.

The critical current of each register junction E, F and G was inferred from operational behavior to be in the approximate range 100 -500;1A.

In operation, with both magnetometer l-V curves displayed on an oscilloscope so that their critical currents could be monitored, current was passed through leads 1-2, starting with zero current and gradually increasing. At a current, typically of the order of l-200p.A, a sudden change in the critical current of the magnetometer A-D was noted. No corresponding change was noted in the critical current of the magnetometer 116. We concluded therefore that a flux quantum (i.e., vortex) entered the register loop 113.

A subsequent decrease of the current in leads 1-2 to zero produced no change the flux quantum remained in the register loop 113. A negative current of sufficient magnitude, again about 100 p.A applied to leads l-2, however, caused the flux quantum to be annihilated in the register loop 113. A still larger negative current introduced a flux quantum of the opposite sign in loop 113. (Note that if a clockwise current can be made to give a positive flux quantum, the same size current counterclockwise will produce a negative flux quantum.)

Similarly current made to flow into lead and out oflead 6 produced analogous results, i.e., a flux quantum entered the register loop 114 but not the register loop 113.

When current was applied to leads 3-4, a different result was observed; namely, that a sufficiently large current caused fiux to suddenly appear in both loops 113 and 114, i.e., a positive flux was placed in the upper loop 113 and negative flux in the loop 114. If there had been a positive flux quantum in the loop 114 initially, this would have cancelled out the negative flux quantum resulting from application of the current to leads 3-4. Consequently, applying current to leads 3-4 caused in effect the transfer of a flux quantum from the loop 113 to loop 114. Thus, a two-stage shift register was demonstrated.

in principle, if the critical currents of the register junctions are all the same and are properly chosen, then the loops can hold only, one, zero, or minus one flux quantum. Application of larger currents to leads l-2 than that required to produce one flux quantum would have the effect of driving flux into the next loop (by passing it along"). lllustratively, a flux quantum is transferred from one register loop to another in a time corresponding to the inverse of the Josephson plasma frequency, i.e., about l0 picoseconds.

The purpose of the silver shunts 110, 111 and 112 will now be discussed. it current is applied to, say, leads 1-2, at the moment when the flux enters the register loop 113 a voltage pulse is developed across the junction E (which is the mechanism for causing currents to flow around the loop). The existence of the pulse at the same time as the current is applied to the leads 1-2 means energy is given to the circuit (f Vidt) of vortices in one-dimension,

which is partially the k LF magnetic energy due to creating a current flowing around the loop 113 and partly a charging of the junction capacitance. This latter charging causes LC oscillations which can have the effect of allowing a second flux quantum to enter loop 113 or of transferring the flux down into the adjoining loop 114. The purpose of the shunts is to damp these oscillations (by providing low resistance in parallel to the junction capacitance).

It is to be understood that the above-described arrangements are merely illustrative of the many possible specific embodiments which can be devised to represent application of the principles of the invention. Numerous and varied other arrangements can be devised in accordance with these principles by those skilled in the art without departing from the spirit and scope of the invention. More particularly, while the preceding embodiments relate specifically to the propagation it is possible to move such vortices in more than one dimension, e.g., in two dimensions in a plane.

What is claimed is:

l. supercurrent apparatus comprising a weak-link supercurrent structure,

creating means for creating in said structure a plurality of magnetic field vortices each characterized by a circulating supercurrent and a flux quantum induced by said supercurrent,

means of establishing in said structure preferred locations about each of which a vortex distributes itself so that a local minimum of the sum of the total magnetic energy plus the Josephson coupling energy is created with respect to such vortex, and

control means for causing selected ones of said vortices to propagate in said structure from one of said preferred locations to another.

2. The apparatus of claim 1 wherein said preferred locations are centered in regions separated by a distance S which to a first approximation satisfies the relationship L1, 1 where L is the self-inductance of a circulating supercurrent path, 1 is the flux quantum supported by the circulating supercurrent and I is the net critical current of a region of length S.

3. The apparatus of claim 1 wherein said control means comprises means for applying control current in control regions near to each of said preselected vortices and in a direction opposite to the flow of supercurrent in said control regions so that said preselected vortices propagate away from said control regions.

4. The apparatus of claim 1 wherein said control means comprises means for applying control current in control regions near to each of said preselected vortices and in the same direction as the flow of supercurrent in said control regions so that said preselected vortices propagate toward said control region.

5. The apparatus of claim 1 wherein said weak-link structure is elongated,

said creating means comprises a current source connected to one end of said structure, and

said control means comprises means for selectively applying control current along the elongated dimension of said structure at spaced points near to said preferred locations so that preselected ones of said vortices are made to move toward the other end of aid structure.

6. The apparatus of claim 5 including utilization means connected to the other end of said structure to detect said vortices as each reaches said other end.

7. The apparatus of claim 6 wherein the output of said creating means comprises a pulse code modulated train of cur- 1'61: pulses, each pulse being separated by a blanking interval, an

saidalcontrol means is turned on during said blanking inter- 8. The apparatus of claim 7 wherein the current from said control means is applied sequentially to each of said spaced points beginning with the point nearest to said other end and ending with the point nearest said one end.

9. The apparatus of claim 7 wherein the current from said control means is applied substantially simultaneously to each of said spaced points.

10. The apparatus of claim 1 wherein each of said preferred locations is a region in which the critical supercurrent is zero.

1 l. The apparatus of claim 10 including a pair of superconductive layers,

a nonsuperconductive layer contiguous with and separating said superconductive layers,

said nonsuperconductive layer having a plurality of apertures extending therethrough between said superconductive layers, said apertures forming said preferred locations and the remaining portions of said nonsuperconductive layer in conjunction with said superconductive layers contiguous therewith forming a plurality of said weak-link regions electrically connected in parallel.

12. The apparatus of claim 11 wherein said nonsuperconductive layer comprises a material selected from the group consisting of insulators and normal metal.

13. The apparatus of claim 10 including a pair of superconductive layers,

a nonsuperconductive layer contiguous with and separating said superconductive layers,

said nonsupercondutive layer having a plurality of separated first regions of thickness effective to prevent supercurrent tunneling therethrough and a plurality of second regions interleaving said first regions and of thickness effective to permit supercurrent tunneling therethrough,

said first regions constituting said preferred locations in which the critical supercurrent is substantially zero and said second regions constituting a plurality of weak-link regions electrically connected in parallel.

14. The apparatus of claim 13 wherein said nonsuperconductive layer comprises a material selected from the group consisting of insulators and normal metals.

15. The apparatus of claim 10 including a first superconductive layer in the form of a strip having a plurality of first appendages of the same material as said strip extending therefrom,

plurality of nonsuperconductive layers, one formed on at least a portion of each of said first appendages,

a second superconductive layer contacting each of said nonsuperconductive layers, thereby forming a plurality of superconducting loops each of which includes a pair of weak-link regions electrically connected in parallel, each of said loops being adapted so that to a first approximation L1, 1 where L is the self inductance of the loop in which a supercurrent flows supporting a flux quantum 1 and I, is the critical current of each of said weak-link regions.

16. The apparatus of claim 15 where said nonsuperconductive layers comprise a material selected from the group consisting of insulators and normal metals.

17. The apparatus of claim 16 including a separate resistive shunt electrically connected in parallel with each of said weak-link regions.

18. The apparatus of claim 17 wherein said creating means comprises a current source connected between a first one .of said first appendages and .said second layer,

said control means includes means for applying a current between said second layer and selected ones of said other first appendages, and including utilization means connected between a different one of said first appendages and said second layer. 19. The apparatus of claim 18 including a separate weaklink magnetometer magnetically coupled to each of said loops.

20. The apparatus of claim 19 wherein said first-appendages are located on one side of said strip and said magnetometers each comprise a pair of second appendages extending from the other side of said strip, opposite one of said loops,

a plurality of nonsuperconductive layers. one formed on a portion of each of said second appendages,

a third superconductive layer contacting each of said nonsuperconductive layers thereby forming a pair of weak-link regions electrically connected in parallel, and

means for detecting changes induced in the critical supercurrent of each of said latter pairs of weak-link regions.

21. The apparatus of claim 1 including a pair of elongated superconductive layers,

an elongated nonsuperconductive third layer of substantially uniform thickness contiguous with and disposed between said superconductive layers, thereby forming an elongated multilayered structure,

means for applying along said third layer a localized magnetic field at a plurality of points equally spaced by a distance of approximately twice the Josephson penetration depth and in a direction substantially parallel to said third layer, thereby defining said preferred locations about which said vortices prefer to distribute themselves, said magnetic field being applied in magnetic sense opposite to that of said vortex in said third layer.

22. The apparatus of claim 21 wherein said creating means comprises a current source connected across said superconductive layer at one end of said structure, and

said control means comprises means for selectively applying a control current near to predetermined ones of said vortices so that said predetermined vortices propagate toward the other end of said structure.

23. The apparatus of claim 22 including utilization means connected across said superconductive layers at the other end of said structure to detect said vortices as each reaches said other end.

24. The apparatus of claim 23 wherein said nonsuperconductive layer comprises a material selected from the group consisting of insulators and normal metals.

25. The apparatus of claim 1 including a first portion in which the critical supercurrent is substantially uniform and nonzero,

contiguous with said first portion, a second portion in which the critical supercurrent is substantially zero and which is characterized by a variable self-inductance per unit length as measured in a direction parallel to the direction of vortex propagation.

26. The apparatus of claim 25 wherein the width of said second portion undulates along a face parallel to said direction of vortex propagation.

27. The apparatus of claim 26 wherein the width of said second portion undulates periodically.

28. The apparatus of claim 27 wherein said first portion comprises a first pair of elongated superconductive layers,

a first elongated nonsuperconductive layer of substantially uniform thickness effective to permit the flow of supercurrent therethrough, said first nonsuperconduc tive layer being contiguous with and disposed between said first pair of superconductive layers, and

said second portion comprises a second pair of superconductive layers,

a second elongated nonsuperconductive layer of substantially uniform thickness effective to prevent the flow of supercurrent therethrough, said second nonsuperconductive layer being contiguous with and disposed between said second pair of superconductive layers,

one elongated face of said first portion being contiguous with one elongated face of said second portion.

29. The apparatus of claim 28 wherein the width of said second portion undulates in the shape of a periodic square wave.

30. The apparatus of claim 28 wherein said creating means comprises a current source connected across said first pair of superconductive layers at one end of said structure, and

said control means comprises means for selectively applying a control current near to predetermined ones of said vortices so that said predetermined vortices propagate toward the other end said structure.

31. The apparatus of claim 30 including utilization means connected across said first pair of superconductive layers at the other end of said structure to detect said vortices as each reaches said other end.

32. The apparatus of claim 31 wherein said nonsuperconductive layers comprise a material selected from the group consisting of insulators and normal metals.

33. For use in weak-link supercurrent apparatus, a structure comprising a plurality of weak-link supercurrent regions electrically connected in parallel to form a plurality of closed circuit paths coupled to one another, adjacent ones of said regions being uniformly separated by a distance S effective to sustain in selected ones of said paths a circulating supercurrent which supports a single magnetic flux quantum linking said path.

34. The structure of claim 33 wherein said distance S is selected so that to a first approximation the following relationship is satisfied where L is the self-inductance of each of said paths, 1 is the flux quantum supported by each circulating supercurrent and I is the net critical current of a region oflength S.

35. The structure of claim 34 including a pair of superconductive layers, a nonsuperconductive layer separating said superconductive layers, said nonsuperconductive layer having a plurality of apertures extending therethrough between said superconductive layers, thereby defining between said apertures a plurality of spaced nonsuperconductive regions which constitute said plurality of weak-link regions connected in parallel. 36. The structure of clam 34 including a pair of superconductive layers a nonsuperconductive layer separating said superconductive layers, said nonsuperconductive layer having a plurality of spaced first regions of thickness effective to prevent supercurrent tunneling therethrough and interleaving said first regions a plurality of second regions of thickness effective to permit supercurrent tunneling therethrough, said second regions constituting said plurality of weak-link regions connected in parallel.

37. For use in weak-link supercurrent apparatus for guiding the propagation of magnetic flux vortices in a first direction, a structure comprising a first portion in which the critical supercurrent is substantially uniform and nonzero,

contiguous with said first portion, a second portion in which the critical supercurrent is substantially zero and which is characterized by a variable self-inductance per unit length as measured in a direction parallel to the direction of vortex propagation.

38. The apparatus of claim 37 where the width of said second portion undulates along a face parallel to said direction of vortex propagation.

39. The apparatus of claim 38 wherein the width of said second portion undulates periodically.

40. The apparatus of claim 39 wherein said first portion comprises a first pair of elongated superconductive layers,

a first elongated nonsuperconductive layer of substantially uniform thickness effective to permit the flow of supercurrent therethrough, said first nonsuperconductive layer being contiguous with and disposed between said first pair of superconductive layers, and

said second portion comprises a second pair of su erconductive layers, a second elongate nonsuperconductive layer of substantially uniform thickness effective to prevent the flow of supercurrent therethrough, said second nonsuperconductive layer being contiguous with and disposed between said second pair of superconductive layers,

one elongated face of said first portion being contiguous with one elongated face of said second portion.

41. The apparatus of claim 40 wherein the width of said second portion undulates in the shape of a periodic square wave. 

1. Supercurrent apparatus comprising a weak-link supercurrent structure, creating means for creating in said structure a plurality of magnetic field vortices each characterized by a circulating supercurrent and a flux quantum induced by said supercurrent, means of establishing in said structure preferred locations about each of which a vortex distributes itself so that a local minimum of the sum of the total magnetic energy plus the Josephson coupling energy is created with respect to such vortex, and control means for causing selected ones of said vortices to propagate in said structure from one of said preferred locations to another.
 2. The apparatus of claim 1 wherein said preferred locations are centered in regions separated by a distance S which to a first approximation satisfies the relationship LIc Phi o where L is the self-inductance of a circulating supercurrent path, Phi o is the flux quantum supported by the circulating supercurrent and Ic is the net critical current of a region of length S.
 3. The apparatus of claim 1 wherein said control means comprises means for applying control current in control regions near to each of said preselected vortices and in a direction opposite to the flow of supercurrent in said control regions so that said preselected vortices propagate away from said control regions.
 4. The apparatus of claim 1 wherein said control means comprises means for applying control current in control regions near to each of said preselected vortices and in the same direction as the flow of supercurrent in said control regions so that said preselected vortices propagate toward said control region.
 5. The apparatus of claim 1 wherein said weak-link structure is elongated, said creating means comprises a current source connected to one end of said structure, and said control means comprises means for selectively applying control current along the elongated dimension of said structure at spaced points near to said preferred locations so that preselected ones of said vortices are made to move toward the other end of aid structure.
 6. The apparatUs of claim 5 including utilization means connected to the other end of said structure to detect said vortices as each reaches said other end.
 7. The apparatus of claim 6 wherein the output of said creating means comprises a pulse code modulated train of current pulses, each pulse being separated by a blanking interval, and said control means is turned on during said blanking intervals.
 8. The apparatus of claim 7 wherein the current from said control means is applied sequentially to each of said spaced points beginning with the point nearest to said other end and ending with the point nearest said one end.
 9. The apparatus of claim 7 wherein the current from said control means is applied substantially simultaneously to each of said spaced points.
 10. The apparatus of claim 1 wherein each of said preferred locations is a region in which the critical supercurrent is zero.
 11. The apparatus of claim 10 including a pair of superconductive layers, a nonsuperconductive layer contiguous with and separating said superconductive layers, said nonsuperconductive layer having a plurality of apertures extending therethrough between said superconductive layers, said apertures forming said preferred locations and the remaining portions of said nonsuperconductive layer in conjunction with said superconductive layers contiguous therewith forming a plurality of said weak-link regions electrically connected in parallel.
 12. The apparatus of claim 11 wherein said nonsuperconductive layer comprises a material selected from the group consisting of insulators and normal metal.
 13. The apparatus of claim 10 including a pair of superconductive layers, a nonsuperconductive layer contiguous with and separating said superconductive layers, said nonsupercondutive layer having a plurality of separated first regions of thickness effective to prevent supercurrent tunneling therethrough and a plurality of second regions interleaving said first regions and of thickness effective to permit supercurrent tunneling therethrough, said first regions constituting said preferred locations in which the critical supercurrent is substantially zero and said second regions constituting a plurality of weak-link regions electrically connected in parallel.
 14. The apparatus of claim 13 wherein said nonsuperconductive layer comprises a material selected from the group consisting of insulators and normal metals.
 15. The apparatus of claim 10 including a first superconductive layer in the form of a strip having a plurality of first appendages of the same material as said strip extending therefrom, plurality of nonsuperconductive layers, one formed on at least a portion of each of said first appendages, a second superconductive layer contacting each of said nonsuperconductive layers, thereby forming a plurality of superconducting loops each of which includes a pair of weak-link regions electrically connected in parallel, each of said loops being adapted so that to a first approximation LIc Phi o where L is the self inductance of the loop in which a supercurrent flows supporting a flux quantum Phi o, and Ic is the critical current of each of said weak-link regions.
 16. The apparatus of claim 15 where said nonsuperconductive layers comprise a material selected from the group consisting of insulators and normal metals.
 17. The apparatus of claim 16 including a separate resistive shunt electrically connected in parallel with each of said weak-link regions.
 18. The apparatus of claim 17 wherein said creating means comprises a current source connected between a first one of said first appendages and said second layer, said control means includes means for applying a current between said second layer and selected ones of said other first appendages, and including utilization means connected between a different one of said first appendages and said second layer.
 19. The appAratus of claim 18 including a separate weak-link magnetometer magnetically coupled to each of said loops.
 20. The apparatus of claim 19 wherein said first appendages are located on one side of said strip and said magnetometers each comprise a pair of second appendages extending from the other side of said strip, opposite one of said loops, a plurality of nonsuperconductive layers, one formed on a portion of each of said second appendages, a third superconductive layer contacting each of said nonsuperconductive layers thereby forming a pair of weak-link regions electrically connected in parallel, and means for detecting changes induced in the critical supercurrent of each of said latter pairs of weak-link regions.
 21. The apparatus of claim 1 including a pair of elongated superconductive layers, an elongated nonsuperconductive third layer of substantially uniform thickness contiguous with and disposed between said superconductive layers, thereby forming an elongated multilayered structure, means for applying along said third layer a localized magnetic field at a plurality of points equally spaced by a distance of approximately twice the Josephson penetration depth and in a direction substantially parallel to said third layer, thereby defining said preferred locations about which said vortices prefer to distribute themselves, said magnetic field being applied in magnetic sense opposite to that of said vortex in said third layer.
 22. The apparatus of claim 21 wherein said creating means comprises a current source connected across said superconductive layer at one end of said structure, and said control means comprises means for selectively applying a control current near to predetermined ones of said vortices so that said predetermined vortices propagate toward the other end of said structure.
 23. The apparatus of claim 22 including utilization means connected across said superconductive layers at the other end of said structure to detect said vortices as each reaches said other end.
 24. The apparatus of claim 23 wherein said nonsuperconductive layer comprises a material selected from the group consisting of insulators and normal metals.
 25. The apparatus of claim 1 including a first portion in which the critical supercurrent is substantially uniform and nonzero, contiguous with said first portion, a second portion in which the critical supercurrent is substantially zero and which is characterized by a variable self-inductance per unit length as measured in a direction parallel to the direction of vortex propagation.
 26. The apparatus of claim 25 wherein the width of said second portion undulates along a face parallel to said direction of vortex propagation.
 27. The apparatus of claim 26 wherein the width of said second portion undulates periodically.
 28. The apparatus of claim 27 wherein said first portion comprises a first pair of elongated superconductive layers, a first elongated nonsuperconductive layer of substantially uniform thickness effective to permit the flow of supercurrent therethrough, said first nonsuperconductive layer being contiguous with and disposed between said first pair of superconductive layers, and said second portion comprises a second pair of superconductive layers, a second elongated nonsuperconductive layer of substantially uniform thickness effective to prevent the flow of supercurrent therethrough, said second nonsuperconductive layer being contiguous with and disposed between said second pair of superconductive layers, one elongated face of said first portion being contiguous with one elongated face of said second portion.
 29. The apparatus of claim 28 wherein the width of said second portion undulates in the shape of a periodic square wave.
 30. The apparatus of claim 28 wherein said creating means comprises a current source connected across said first pair of superconductive layers at one end of said strucTure, and said control means comprises means for selectively applying a control current near to predetermined ones of said vortices so that said predetermined vortices propagate toward the other end said structure.
 31. The apparatus of claim 30 including utilization means connected across said first pair of superconductive layers at the other end of said structure to detect said vortices as each reaches said other end.
 32. The apparatus of claim 31 wherein said nonsuperconductive layers comprise a material selected from the group consisting of insulators and normal metals.
 33. For use in weak-link supercurrent apparatus, a structure comprising a plurality of weak-link supercurrent regions electrically connected in parallel to form a plurality of closed circuit paths coupled to one another, adjacent ones of said regions being uniformly separated by a distance S effective to sustain in selected ones of said paths a circulating supercurrent which supports a single magnetic flux quantum linking said path.
 34. The structure of claim 33 wherein said distance S is selected so that to a first approximation the following relationship is satisfied LIc Phi o where L is the self-inductance of each of said paths, Phi o is the flux quantum supported by each circulating supercurrent and Ic is the net critical current of a region of length S.
 35. The structure of claim 34 including a pair of superconductive layers, a nonsuperconductive layer separating said superconductive layers, said nonsuperconductive layer having a plurality of apertures extending therethrough between said superconductive layers, thereby defining between said apertures a plurality of spaced nonsuperconductive regions which constitute said plurality of weak-link regions connected in parallel.
 36. The structure of clam 34 including a pair of superconductive layers a nonsuperconductive layer separating said superconductive layers, said nonsuperconductive layer having a plurality of spaced first regions of thickness effective to prevent supercurrent tunneling therethrough and interleaving said first regions a plurality of second regions of thickness effective to permit supercurrent tunneling therethrough, said second regions constituting said plurality of weak-link regions connected in parallel.
 37. For use in weak-link supercurrent apparatus for guiding the propagation of magnetic flux vortices in a first direction, a structure comprising a first portion in which the critical supercurrent is substantially uniform and nonzero, contiguous with said first portion, a second portion in which the critical supercurrent is substantially zero and which is characterized by a variable self-inductance per unit length as measured in a direction parallel to the direction of vortex propagation.
 38. The apparatus of claim 37 where the width of said second portion undulates along a face parallel to said direction of vortex propagation.
 39. The apparatus of claim 38 wherein the width of said second portion undulates periodically.
 40. The apparatus of claim 39 wherein said first portion comprises a first pair of elongated superconductive layers, a first elongated nonsuperconductive layer of substantially uniform thickness effective to permit the flow of supercurrent therethrough, said first nonsuperconductive layer being contiguous with and disposed between said first pair of superconductive layers, and said second portion comprises a second pair of superconductive layers, a second elongated nonsuperconductive layer of substantially uniform thickness effective to prevent the flow of supercurrent therethrough, said second nonsuperconductive layer being contiguous with and disposed between said second pair of superconductive layers, one elongated face of said first portion being contiguous with one elongated face of said second portion.
 41. The apparatus of claim 40 whErein the width of said second portion undulates in the shape of a periodic square wave. 